Python access to Skin Modifier data - again
The original question you link to mentions this in the first line, but doesn't make a point to clarify why the Object/Edit mode switch is important.

Non BMesh

When using obj.data.skin_vertices[0].data, the Skin Modifier data will show the correct current values only when the object is put back in Object Mode. The same is also true for checking other information of the mesh, like vertex.select.

BMesh

It may be possible to get this skin information while still in Edit Mode using bm = bmesh.from_edit_mesh(obj.data) but I have not been able to find an obvious way. If it is possible someone will no doubt offer a suggestion.